ATOOLS/Math/Lorentz_Ten4.H

0001 #ifndef ATOOLS_Math_Lorentz_Ten4_H
0002 #define ATOOLS_Math_Lorentz_Ten4_H
0003
0004 #include "ATOOLS/Math/MathTools.H"
0005
0006 namespace ATOOLS {
0007   template<typename Scalar> class Lorentz_Ten3;
0008
0009   template<typename Scalar>
0010   class Lorentz_Ten4 {
0011     Scalar m_x[4][4][4][4];
0012   public:
0013     inline Lorentz_Ten4() {}
0014     inline Lorentz_Ten4(const Scalar& s) {
0015       for (unsigned short int i=0; i<4; ++i)
0016         for (unsigned short int j=0; j<4; ++j)
0017           for (unsigned short int k=0; k<4; ++k)
0018             for (unsigned short int l=0; l<4; ++l)
0019               m_x[i][j][k][l] = s;
0020     }
0021     template<typename Scalar2>
0022     inline Lorentz_Ten4(const Lorentz_Ten4<Scalar2> & ten) {
0023       for (unsigned short int i=0; i<4; ++i)
0024         for (unsigned short int j=0; j<4; ++j)
0025           for (unsigned short int k=0; k<4; ++k)
0026             for (unsigned short int l=0; l<4; ++l)
0027               m_x[i][j][k][l] = ten.at(i,j,k,l);
0028     }
0029     inline Lorentz_Ten4(
0030           const Scalar& x0000, const Scalar& x1000, const Scalar& x2000, const Scalar& x3000,
0031           const Scalar& x0100, const Scalar& x1100, const Scalar& x2100, const Scalar& x3100,
0032           const Scalar& x0200, const Scalar& x1200, const Scalar& x2200, const Scalar& x3200,
0033           const Scalar& x0300, const Scalar& x1300, const Scalar& x2300, const Scalar& x3300,
0034
0035           const Scalar& x0010, const Scalar& x1010, const Scalar& x2010, const Scalar& x3010,
0036           const Scalar& x0110, const Scalar& x1110, const Scalar& x2110, const Scalar& x3110,
0037           const Scalar& x0210, const Scalar& x1210, const Scalar& x2210, const Scalar& x3210,
0038           const Scalar& x0310, const Scalar& x1310, const Scalar& x2310, const Scalar& x3310,
0039
0040           const Scalar& x0020, const Scalar& x1020, const Scalar& x2020, const Scalar& x3020,
0041           const Scalar& x0120, const Scalar& x1120, const Scalar& x2120, const Scalar& x3120,
0042           const Scalar& x0220, const Scalar& x1220, const Scalar& x2220, const Scalar& x3220,
0043           const Scalar& x0320, const Scalar& x1320, const Scalar& x2320, const Scalar& x3320,
0044
0045           const Scalar& x0030, const Scalar& x1030, const Scalar& x2030, const Scalar& x3030,
0046           const Scalar& x0130, const Scalar& x1130, const Scalar& x2130, const Scalar& x3130,
0047           const Scalar& x0230, const Scalar& x1230, const Scalar& x2230, const Scalar& x3230,
0048           const Scalar& x0330, const Scalar& x1330, const Scalar& x2330, const Scalar& x3330,
0049
0050           const Scalar& x0001, const Scalar& x1001, const Scalar& x2001, const Scalar& x3001,
0051           const Scalar& x0101, const Scalar& x1101, const Scalar& x2101, const Scalar& x3101,
0052           const Scalar& x0201, const Scalar& x1201, const Scalar& x2201, const Scalar& x3201,
0053           const Scalar& x0301, const Scalar& x1301, const Scalar& x2301, const Scalar& x3301,
0054
0055           const Scalar& x0011, const Scalar& x1011, const Scalar& x2011, const Scalar& x3011,
0056           const Scalar& x0111, const Scalar& x1111, const Scalar& x2111, const Scalar& x3111,
0057           const Scalar& x0211, const Scalar& x1211, const Scalar& x2211, const Scalar& x3211,
0058           const Scalar& x0311, const Scalar& x1311, const Scalar& x2311, const Scalar& x3311,
0059
0060           const Scalar& x0021, const Scalar& x1021, const Scalar& x2021, const Scalar& x3021,
0061           const Scalar& x0121, const Scalar& x1121, const Scalar& x2121, const Scalar& x3121,
0062           const Scalar& x0221, const Scalar& x1221, const Scalar& x2221, const Scalar& x3221,
0063           const Scalar& x0321, const Scalar& x1321, const Scalar& x2321, const Scalar& x3321,
0064
0065           const Scalar& x0031, const Scalar& x1031, const Scalar& x2031, const Scalar& x3031,
0066           const Scalar& x0131, const Scalar& x1131, const Scalar& x2131, const Scalar& x3131,
0067           const Scalar& x0231, const Scalar& x1231, const Scalar& x2231, const Scalar& x3231,
0068           const Scalar& x0331, const Scalar& x1331, const Scalar& x2331, const Scalar& x3331,
0069
0070           const Scalar& x0002, const Scalar& x1002, const Scalar& x2002, const Scalar& x3002,
0071           const Scalar& x0102, const Scalar& x1102, const Scalar& x2102, const Scalar& x3102,
0072           const Scalar& x0202, const Scalar& x1202, const Scalar& x2202, const Scalar& x3202,
0073           const Scalar& x0302, const Scalar& x1302, const Scalar& x2302, const Scalar& x3302,
0074
0075           const Scalar& x0012, const Scalar& x1012, const Scalar& x2012, const Scalar& x3012,
0076           const Scalar& x0112, const Scalar& x1112, const Scalar& x2112, const Scalar& x3112,
0077           const Scalar& x0212, const Scalar& x1212, const Scalar& x2212, const Scalar& x3212,
0078           const Scalar& x0312, const Scalar& x1312, const Scalar& x2312, const Scalar& x3312,
0079
0080           const Scalar& x0022, const Scalar& x1022, const Scalar& x2022, const Scalar& x3022,
0081           const Scalar& x0122, const Scalar& x1122, const Scalar& x2122, const Scalar& x3122,
0082           const Scalar& x0222, const Scalar& x1222, const Scalar& x2222, const Scalar& x3222,
0083           const Scalar& x0322, const Scalar& x1322, const Scalar& x2322, const Scalar& x3322,
0084
0085           const Scalar& x0032, const Scalar& x1032, const Scalar& x2032, const Scalar& x3032,
0086           const Scalar& x0132, const Scalar& x1132, const Scalar& x2132, const Scalar& x3132,
0087           const Scalar& x0232, const Scalar& x1232, const Scalar& x2232, const Scalar& x3232,
0088           const Scalar& x0332, const Scalar& x1332, const Scalar& x2332, const Scalar& x3332,
0089
0090           const Scalar& x0003, const Scalar& x1003, const Scalar& x2003, const Scalar& x3003,
0091           const Scalar& x0103, const Scalar& x1103, const Scalar& x2103, const Scalar& x3103,
0092           const Scalar& x0203, const Scalar& x1203, const Scalar& x2203, const Scalar& x3203,
0093           const Scalar& x0303, const Scalar& x1303, const Scalar& x2303, const Scalar& x3303,
0094
0095           const Scalar& x0013, const Scalar& x1013, const Scalar& x2013, const Scalar& x3013,
0096           const Scalar& x0113, const Scalar& x1113, const Scalar& x2113, const Scalar& x3113,
0097           const Scalar& x0213, const Scalar& x1213, const Scalar& x2213, const Scalar& x3213,
0098           const Scalar& x0313, const Scalar& x1313, const Scalar& x2313, const Scalar& x3313,
0099
0100           const Scalar& x0023, const Scalar& x1023, const Scalar& x2023, const Scalar& x3023,
0101           const Scalar& x0123, const Scalar& x1123, const Scalar& x2123, const Scalar& x3123,
0102           const Scalar& x0223, const Scalar& x1223, const Scalar& x2223, const Scalar& x3223,
0103           const Scalar& x0323, const Scalar& x1323, const Scalar& x2323, const Scalar& x3323,
0104
0105           const Scalar& x0033, const Scalar& x1033, const Scalar& x2033, const Scalar& x3033,
0106           const Scalar& x0133, const Scalar& x1133, const Scalar& x2133, const Scalar& x3133,
0107           const Scalar& x0233, const Scalar& x1233, const Scalar& x2233, const Scalar& x3233,
0108           const Scalar& x0333, const Scalar& x1333, const Scalar& x2333, const Scalar& x3333
0109             ) {
0110    m_x[0][0][0][0]=x0000; m_x[1][0][0][0]=x1000; m_x[2][0][0][0]=x2000; m_x[3][0][0][0]=x3000;
0111    m_x[0][1][0][0]=x0100; m_x[1][1][0][0]=x1100; m_x[2][1][0][0]=x2100; m_x[3][1][0][0]=x3100;
0112    m_x[0][2][0][0]=x0200; m_x[1][2][0][0]=x1200; m_x[2][2][0][0]=x2200; m_x[3][2][0][0]=x3200;
0113    m_x[0][3][0][0]=x0300; m_x[1][3][0][0]=x1300; m_x[2][3][0][0]=x2300; m_x[3][3][0][0]=x3300;
0114
0115    m_x[0][0][1][0]=x0010; m_x[1][0][1][0]=x1010; m_x[2][0][1][0]=x2010; m_x[3][0][1][0]=x3010;
0116    m_x[0][1][1][0]=x0110; m_x[1][1][1][0]=x1110; m_x[2][1][1][0]=x2110; m_x[3][1][1][0]=x3110;
0117    m_x[0][2][1][0]=x0210; m_x[1][2][1][0]=x1210; m_x[2][2][1][0]=x2210; m_x[3][2][1][0]=x3210;
0118    m_x[0][3][1][0]=x0310; m_x[1][3][1][0]=x1310; m_x[2][3][1][0]=x2310; m_x[3][3][1][0]=x3310;
0119
0120    m_x[0][0][2][0]=x0020; m_x[1][0][2][0]=x1020; m_x[2][0][2][0]=x2020; m_x[3][0][2][0]=x3020;
0121    m_x[0][1][2][0]=x0120; m_x[1][1][2][0]=x1120; m_x[2][1][2][0]=x2120; m_x[3][1][2][0]=x3120;
0122    m_x[0][2][2][0]=x0220; m_x[1][2][2][0]=x1220; m_x[2][2][2][0]=x2220; m_x[3][2][2][0]=x3220;
0123    m_x[0][3][2][0]=x0320; m_x[1][3][2][0]=x1320; m_x[2][3][2][0]=x2320; m_x[3][3][2][0]=x3320;
0124
0125    m_x[0][0][3][0]=x0030; m_x[1][0][3][0]=x1030; m_x[2][0][3][0]=x2030; m_x[3][0][3][0]=x3030;
0126    m_x[0][1][3][0]=x0130; m_x[1][1][3][0]=x1130; m_x[2][1][3][0]=x2130; m_x[3][1][3][0]=x3130;
0127    m_x[0][2][3][0]=x0230; m_x[1][2][3][0]=x1230; m_x[2][2][3][0]=x2230; m_x[3][2][3][0]=x3230;
0128    m_x[0][3][3][0]=x0330; m_x[1][3][3][0]=x1330; m_x[2][3][3][0]=x2330; m_x[3][3][3][0]=x3330;
0129
0130    m_x[0][0][0][1]=x0001; m_x[1][0][0][1]=x1001; m_x[2][0][0][1]=x2001; m_x[3][0][0][1]=x3001;
0131    m_x[0][1][0][1]=x0101; m_x[1][1][0][1]=x1101; m_x[2][1][0][1]=x2101; m_x[3][1][0][1]=x3101;
0132    m_x[0][2][0][1]=x0201; m_x[1][2][0][1]=x1201; m_x[2][2][0][1]=x2201; m_x[3][2][0][1]=x3201;
0133    m_x[0][3][0][1]=x0301; m_x[1][3][0][1]=x1301; m_x[2][3][0][1]=x2301; m_x[3][3][0][1]=x3301;
0134
0135    m_x[0][0][1][1]=x0011; m_x[1][0][1][1]=x1011; m_x[2][0][1][1]=x2011; m_x[3][0][1][1]=x3011;
0136    m_x[0][1][1][1]=x0111; m_x[1][1][1][1]=x1111; m_x[2][1][1][1]=x2111; m_x[3][1][1][1]=x3111;
0137    m_x[0][2][1][1]=x0211; m_x[1][2][1][1]=x1211; m_x[2][2][1][1]=x2211; m_x[3][2][1][1]=x3211;
0138    m_x[0][3][1][1]=x0311; m_x[1][3][1][1]=x1311; m_x[2][3][1][1]=x2311; m_x[3][3][1][1]=x3311;
0139
0140    m_x[0][0][2][1]=x0021; m_x[1][0][2][1]=x1021; m_x[2][0][2][1]=x2021; m_x[3][0][2][1]=x3021;
0141    m_x[0][1][2][1]=x0121; m_x[1][1][2][1]=x1121; m_x[2][1][2][1]=x2121; m_x[3][1][2][1]=x3121;
0142    m_x[0][2][2][1]=x0221; m_x[1][2][2][1]=x1221; m_x[2][2][2][1]=x2221; m_x[3][2][2][1]=x3221;
0143    m_x[0][3][2][1]=x0321; m_x[1][3][2][1]=x1321; m_x[2][3][2][1]=x2321; m_x[3][3][2][1]=x3321;
0144
0145    m_x[0][0][3][1]=x0031; m_x[1][0][3][1]=x1031; m_x[2][0][3][1]=x2031; m_x[3][0][3][1]=x3031;
0146    m_x[0][1][3][1]=x0131; m_x[1][1][3][1]=x1131; m_x[2][1][3][1]=x2131; m_x[3][1][3][1]=x3131;
0147    m_x[0][2][3][1]=x0231; m_x[1][2][3][1]=x1231; m_x[2][2][3][1]=x2231; m_x[3][2][3][1]=x3231;
0148    m_x[0][3][3][1]=x0331; m_x[1][3][3][1]=x1331; m_x[2][3][3][1]=x2331; m_x[3][3][3][1]=x3331;
0149
0150    m_x[0][0][0][2]=x0002; m_x[1][0][0][2]=x1002; m_x[2][0][0][2]=x2002; m_x[3][0][0][2]=x3002;
0151    m_x[0][1][0][2]=x0102; m_x[1][1][0][2]=x1102; m_x[2][1][0][2]=x2102; m_x[3][1][0][2]=x3102;
0152    m_x[0][2][0][2]=x0202; m_x[1][2][0][2]=x1202; m_x[2][2][0][2]=x2202; m_x[3][2][0][2]=x3202;
0153    m_x[0][3][0][2]=x0302; m_x[1][3][0][2]=x1302; m_x[2][3][0][2]=x2302; m_x[3][3][0][2]=x3302;
0154
0155    m_x[0][0][1][2]=x0012; m_x[1][0][1][2]=x1012; m_x[2][0][1][2]=x2012; m_x[3][0][1][2]=x3012;
0156    m_x[0][1][1][2]=x0112; m_x[1][1][1][2]=x1112; m_x[2][1][1][2]=x2112; m_x[3][1][1][2]=x3112;
0157    m_x[0][2][1][2]=x0212; m_x[1][2][1][2]=x1212; m_x[2][2][1][2]=x2212; m_x[3][2][1][2]=x3212;
0158    m_x[0][3][1][2]=x0312; m_x[1][3][1][2]=x1312; m_x[2][3][1][2]=x2312; m_x[3][3][1][2]=x3312;
0159
0160    m_x[0][0][2][2]=x0022; m_x[1][0][2][2]=x1022; m_x[2][0][2][2]=x2022; m_x[3][0][2][2]=x3022;
0161    m_x[0][1][2][2]=x0122; m_x[1][1][2][2]=x1122; m_x[2][1][2][2]=x2122; m_x[3][1][2][2]=x3122;
0162    m_x[0][2][2][2]=x0222; m_x[1][2][2][2]=x1222; m_x[2][2][2][2]=x2222; m_x[3][2][2][2]=x3222;
0163    m_x[0][3][2][2]=x0322; m_x[1][3][2][2]=x1322; m_x[2][3][2][2]=x2322; m_x[3][3][2][2]=x3322;
0164
0165    m_x[0][0][3][2]=x0032; m_x[1][0][3][2]=x1032; m_x[2][0][3][2]=x2032; m_x[3][0][3][2]=x3032;
0166    m_x[0][1][3][2]=x0132; m_x[1][1][3][2]=x1132; m_x[2][1][3][2]=x2132; m_x[3][1][3][2]=x3132;
0167    m_x[0][2][3][2]=x0232; m_x[1][2][3][2]=x1232; m_x[2][2][3][2]=x2232; m_x[3][2][3][2]=x3232;
0168    m_x[0][3][3][2]=x0332; m_x[1][3][3][2]=x1332; m_x[2][3][3][2]=x2332; m_x[3][3][3][2]=x3332;
0169
0170    m_x[0][0][0][3]=x0003; m_x[1][0][0][3]=x1003; m_x[2][0][0][3]=x2003; m_x[3][0][0][3]=x3003;
0171    m_x[0][1][0][3]=x0103; m_x[1][1][0][3]=x1103; m_x[2][1][0][3]=x2103; m_x[3][1][0][3]=x3103;
0172    m_x[0][2][0][3]=x0203; m_x[1][2][0][3]=x1203; m_x[2][2][0][3]=x2203; m_x[3][2][0][3]=x3203;
0173    m_x[0][3][0][3]=x0303; m_x[1][3][0][3]=x1303; m_x[2][3][0][3]=x2303; m_x[3][3][0][3]=x3303;
0174
0175    m_x[0][0][1][3]=x0013; m_x[1][0][1][3]=x1013; m_x[2][0][1][3]=x2013; m_x[3][0][1][3]=x3013;
0176    m_x[0][1][1][3]=x0113; m_x[1][1][1][3]=x1113; m_x[2][1][1][3]=x2113; m_x[3][1][1][3]=x3113;
0177    m_x[0][2][1][3]=x0213; m_x[1][2][1][3]=x1213; m_x[2][2][1][3]=x2213; m_x[3][2][1][3]=x3213;
0178    m_x[0][3][1][3]=x0313; m_x[1][3][1][3]=x1313; m_x[2][3][1][3]=x2313; m_x[3][3][1][3]=x3313;
0179
0180    m_x[0][0][2][3]=x0023; m_x[1][0][2][3]=x1023; m_x[2][0][2][3]=x2023; m_x[3][0][2][3]=x3023;
0181    m_x[0][1][2][3]=x0123; m_x[1][1][2][3]=x1123; m_x[2][1][2][3]=x2123; m_x[3][1][2][3]=x3123;
0182    m_x[0][2][2][3]=x0223; m_x[1][2][2][3]=x1223; m_x[2][2][2][3]=x2223; m_x[3][2][2][3]=x3223;
0183    m_x[0][3][2][3]=x0323; m_x[1][3][2][3]=x1323; m_x[2][3][2][3]=x2323; m_x[3][3][2][3]=x3323;
0184
0185    m_x[0][0][3][3]=x0033; m_x[1][0][3][3]=x1033; m_x[2][0][3][3]=x2033; m_x[3][0][3][3]=x3033;
0186    m_x[0][1][3][3]=x0133; m_x[1][1][3][3]=x1133; m_x[2][1][3][3]=x2133; m_x[3][1][3][3]=x3133;
0187    m_x[0][2][3][3]=x0233; m_x[1][2][3][3]=x1233; m_x[2][2][3][3]=x2233; m_x[3][2][3][3]=x3233;
0188    m_x[0][3][3][3]=x0333; m_x[1][3][3][3]=x1333; m_x[2][3][3][3]=x2333; m_x[3][3][3][3]=x3333;
0189     }
0190     inline Lorentz_Ten4(const Scalar ten[4][4][4][4]) {
0191       for (unsigned short int i=0; i<4; ++i)
0192         for (unsigned short int j=0; j<4; ++j)
0193           for (unsigned short int k=0; k<4; ++k)
0194             for (unsigned short int l=0; l<4; ++l)
0195               m_x[i][j][k][l] = ten[i][j][k][l];
0196     }
0197
0198     // element extraction
0199     inline const Scalar at(unsigned short int i, unsigned short int j,
0200                            unsigned short int k, unsigned short int l) const {
0201       return m_x[i][j][k][l];
0202     }
0203
0204 //     typedef Scalar (*ScalarArray)[4][4][4];
0205 //     inline ScalarArray operator[] (unsigned short int i) {
0206 //       return m_x[i];
0207 //     }
0208
0209 //     inline Lorentz_Ten3<Scalar> operator[] (unsigned short int i) {
0210 //       return Lorentz_Ten3<Scalar>(***m_x[i]);
0211 //     }
0212
0213 //     inline const Scalar *** operator[] (unsigned short int i) const {
0214 //       return m_x[i];
0215 //     }
0216
0217     // sign flip
0218     inline Lorentz_Ten4<Scalar> operator-() const {
0219       Scalar x[4][4][4][4];
0220       for (unsigned short int i=0; i<4; ++i)
0221         for (unsigned short int j=0; j<4; ++j)
0222           for (unsigned short int k=0; k<4; ++k)
0223             for (unsigned short int l=0; l<4; ++l)
0224               x[i][j][k][l] = -m_x.at(i,j,k,l);
0225       return Lorentz_Ten4<Scalar>(x);
0226     }
0227
0228     // transpose pair of indizes
0229     inline Lorentz_Ten4<Scalar> Transpose(unsigned short int a, unsigned short int b) const {
0230       Scalar x[4][4][4][4];
0231       if      (((a==1) && (b==2)) || ((a==2) && (b==1)))
0232         for (unsigned short int i=0; i<4; ++i)
0233           for (unsigned short int j=0; j<4; ++j)
0234             for (unsigned short int k=0; k<4; ++k)
0235               for (unsigned short int l=0; l<4; ++l)
0236                 x[i][j][k][l] = m_x[j][i][k][l];
0237       else if (((a==1) && (b==3)) || ((a==3) && (b==1)))
0238         for (unsigned short int i=0; i<4; ++i)
0239           for (unsigned short int j=0; j<4; ++j)
0240             for (unsigned short int k=0; k<4; ++k)
0241               for (unsigned short int l=0; l<4; ++l)
0242                 x[i][j][k][l] = m_x[k][j][i][l];
0243       else if (((a==1) && (b==4)) || ((a==4) && (b==1)))
0244         for (unsigned short int i=0; i<4; ++i)
0245           for (unsigned short int j=0; j<4; ++j)
0246             for (unsigned short int k=0; k<4; ++k)
0247               for (unsigned short int l=0; l<4; ++l)
0248                 x[i][j][k][l] = m_x[l][j][k][i];
0249       else if (((a==2) && (b==3)) || ((a==3) && (b==2)))
0250         for (unsigned short int i=0; i<4; ++i)
0251           for (unsigned short int j=0; j<4; ++j)
0252             for (unsigned short int k=0; k<4; ++k)
0253               for (unsigned short int l=0; l<4; ++l)
0254                 x[i][j][k][l] = m_x[i][k][j][l];
0255       else if (((a==2) && (b==4)) || ((a==4) && (b==2)))
0256         for (unsigned short int i=0; i<4; ++i)
0257           for (unsigned short int j=0; j<4; ++j)
0258             for (unsigned short int k=0; k<4; ++k)
0259               for (unsigned short int l=0; l<4; ++l)
0260                 x[i][j][k][l] = m_x[i][l][k][j];
0261       else if (((a==3) && (b==4)) || ((a==4) && (b==3)))
0262         for (unsigned short int i=0; i<4; ++i)
0263           for (unsigned short int j=0; j<4; ++j)
0264             for (unsigned short int k=0; k<4; ++k)
0265               for (unsigned short int l=0; l<4; ++l)
0266                 x[i][j][k][l] = m_x[i][j][l][k];
0267       return Lorentz_Ten4<Scalar>(x);
0268     }
0269
0270     // addition/subtraction operators
0271     inline Lorentz_Ten4<Scalar>& operator+=(const Lorentz_Ten4<Scalar>& t) {
0272       for (unsigned short int i=0; i<4; ++i)
0273         for (unsigned short int j=0; j<4; ++j)
0274           for (unsigned short int k=0; k<4; ++k)
0275             for (unsigned short int l=0; l<4; ++l)
0276               m_x[i][j][k][l] += t.at(i,j,k,l);
0277       return *this;
0278     }
0279
0280     inline Lorentz_Ten4<Scalar>& operator-=(const Lorentz_Ten4<Scalar>& t) {
0281       for (unsigned short int i=0; i<4; ++i)
0282         for (unsigned short int j=0; j<4; ++j)
0283           for (unsigned short int k=0; k<4; ++k)
0284             for (unsigned short int l=0; l<4; ++l)
0285               m_x[i][j][k][l] -= t.at(i,j,k,l);
0286       return *this;
0287     }
0288
0289     template<typename Scalar2>
0290     inline Lorentz_Ten4<PROMOTE(Scalar,Scalar2)>
0291     operator+ (const Lorentz_Ten4<Scalar2>& ten) const {
0292       PROMOTE(Scalar,Scalar2) x[4][4][4][4];
0293       for (unsigned short int i=0; i<4; ++i)
0294         for (unsigned short int j=0; j<4; ++j)
0295           for (unsigned short int k=0; k<4; ++k)
0296             for (unsigned short int l=0; l<4; ++l)
0297               x[i][j][k][l] = m_x[i][j][k][l]+ten.at(i,j,k,l);
0298       return Lorentz_Ten4<PROMOTE(Scalar,Scalar2)>(x);
0299     }
0300
0301     template<typename Scalar2>
0302     inline Lorentz_Ten4<PROMOTE(Scalar,Scalar2)>
0303     operator- (const Lorentz_Ten4<Scalar2>& ten) const {
0304       PROMOTE(Scalar,Scalar2) x[4][4][4][4];
0305       for (unsigned short int i=0; i<4; ++i)
0306         for (unsigned short int j=0; j<4; ++j)
0307           for (unsigned short int k=0; k<4; ++k)
0308             for (unsigned short int l=0; l<4; ++l)
0309               x[i][j][k][l] = m_x[i][j][k][l]-ten.at(i,j,k,l);
0310       return Lorentz_Ten4<PROMOTE(Scalar,Scalar2)>(x);
0311     }
0312
0313     // multiplication operators
0314     inline Lorentz_Ten4<Scalar>& operator*= (const Scalar& scal) {
0315       for (unsigned short int i=0; i<4; ++i)
0316         for (unsigned short int j=0; j<4; ++j)
0317           for (unsigned short int k=0; k<4; ++k)
0318             for (unsigned short int l=0; l<4; ++l)
0319               m_x[i][j][k][l] *= scal;
0320       return *this;
0321     }
0322
0323     template<typename Scalar2>
0324     inline Lorentz_Ten4<PROMOTE(Scalar,Scalar2)> operator* (const Scalar2 scal) const {
0325       PROMOTE(Scalar,Scalar2) x[4][4][4][4];
0326       for (unsigned short int i=0; i<4; ++i)
0327         for (unsigned short int j=0; j<4; ++j)
0328           for (unsigned short int k=0; k<4; ++k)
0329             for (unsigned short int l=0; l<4; ++l)
0330               x[i][j][k][l] = scal*m_x[i][j][k][l];
0331       return Lorentz_Ten4<PROMOTE(Scalar,Scalar2)>(x);
0332     }
0333
0334     template<typename Scalar2>
0335     inline Lorentz_Ten4<PROMOTE(Scalar,Scalar2)> operator/ (const Scalar2 scal) const {
0336       return (*this)*(1./scal);
0337     }
0338
0339     inline bool Nan() const {
0340       for (unsigned short int i=0; i<4; ++i)
0341         for (unsigned short int j=0; j<4; ++j)
0342           for (unsigned short int k=0; k<4; ++k)
0343             for (unsigned short int l=0; l<4; ++l)
0344               if (ATOOLS::IsNan<Scalar>(m_x[i][j][k][l])) return true;
0345       return false;
0346     }
0347
0348     inline bool IsZero() const {
0349       for (unsigned short int i=0; i<4; ++i)
0350         for (unsigned short int j=0; j<4; ++j)
0351           for (unsigned short int k=0; k<4; ++k)
0352             for (unsigned short int l=0; l<4; ++l)
0353               if (!ATOOLS::IsZero<Scalar>(m_x[i][j][k][l])) return false;
0354       return true;
0355     }
0356   };
0357
0358   template<typename Scalar,typename Scal2>
0359   inline Lorentz_Ten4<PROMOTE(Scalar,Scal2)>
0360   operator* (const Scal2 s, const Lorentz_Ten4<Scalar>& t) {
0361     return Lorentz_Ten4<PROMOTE(Scalar,Scal2)>(t*s);
0362   }
0363
0364   template<typename Scalar>
0365   std::ostream& operator<<(std::ostream& s, const Lorentz_Ten4<Scalar>& ten) {
0366     return s<<"not implemented for tensors of fourth rank ... "
0367             <<"please project to second rank and display then ..."<<std::endl;
0368   }
0369 }
0370
0371 /*!
0372  \file
0373  \brief   contains class Lorentz_Ten4
0374 */
0375
0376 /*!
0377  \class Lorentz_Ten4<Scalar>
0378  \brief implementation of a 4 dimensional Minkowski 2nd rank tensor and its algebraic
0379  operations
0380
0381  This class can be used as Minkowski 2nd rank tensor with arbitrary scalar types.
0382  All necessary operations, e.g. addition, scalar multiplication, contractions
0383  with other 2nd rank tensor or vectors, etc. are available.
0384  If you want to use this 2nd rank tensor for a new scalar type, you might have to
0385  implement specific functions for this type in MathTools.H.
0386  "Fallback" types for operations with two 2nd rank tensors of different types, e. g.
0387  "complex and double become complex" have to be specified in MathTools.H as
0388  well, see the DECLARE_PROMOTE macro.
0389 */
0390
0391 /*!
0392  \fn Lorentz_Ten4::Lorentz_Ten4()
0393  \brief Standard Constructor
0394 */
0395
0396 /*!
0397  \fn Lorentz_Ten4::Lorentz_Ten4(
0398   const Scalar &x0000, const Scalar &x1000, const Scalar &x2000, const Scalar &x3000,
0399   const Scalar &x0100, const Scalar &x1100, const Scalar &x2100, const Scalar &x3100,
0400   const Scalar &x0200, const Scalar &x1200, const Scalar &x2200, const Scalar &x3200,
0401   const Scalar &x0300, const Scalar &x1300, const Scalar &x2300, const Scalar &x3300,
0402   const Scalar &x0010, const Scalar &x1010, const Scalar &x2010, const Scalar &x3010,
0403   const Scalar &x0110, const Scalar &x1110, const Scalar &x2110, const Scalar &x3110,
0404   const Scalar &x0210, const Scalar &x1210, const Scalar &x2210, const Scalar &x3210,
0405   const Scalar &x0310, const Scalar &x1310, const Scalar &x2310, const Scalar &x3310,
0406   const Scalar &x0020, const Scalar &x1020, const Scalar &x2020, const Scalar &x3020,
0407   const Scalar &x0120, const Scalar &x1120, const Scalar &x2120, const Scalar &x3120,
0408   const Scalar &x0220, const Scalar &x1220, const Scalar &x2220, const Scalar &x3220,
0409   const Scalar &x0320, const Scalar &x1320, const Scalar &x2320, const Scalar &x3320,
0410   const Scalar &x0030, const Scalar &x1030, const Scalar &x2030, const Scalar &x3030,
0411   const Scalar &x0130, const Scalar &x1130, const Scalar &x2130, const Scalar &x3130,
0412   const Scalar &x0230, const Scalar &x1230, const Scalar &x2230, const Scalar &x3230,
0413   const Scalar &x0330, const Scalar &x1330, const Scalar &x2330, const Scalar &x3330,
0414   const Scalar &x0001, const Scalar &x1001, const Scalar &x2001, const Scalar &x3001,
0415   const Scalar &x0101, const Scalar &x1101, const Scalar &x2101, const Scalar &x3101,
0416   const Scalar &x0201, const Scalar &x1201, const Scalar &x2201, const Scalar &x3201,
0417   const Scalar &x0301, const Scalar &x1301, const Scalar &x2301, const Scalar &x3301,
0418   const Scalar &x0011, const Scalar &x1011, const Scalar &x2011, const Scalar &x3011,
0419   const Scalar &x0111, const Scalar &x1111, const Scalar &x2111, const Scalar &x3111,
0420   const Scalar &x0211, const Scalar &x1211, const Scalar &x2211, const Scalar &x3211,
0421   const Scalar &x0311, const Scalar &x1311, const Scalar &x2311, const Scalar &x3311,
0422   const Scalar &x0021, const Scalar &x1021, const Scalar &x2021, const Scalar &x3021,
0423   const Scalar &x0121, const Scalar &x1121, const Scalar &x2121, const Scalar &x3121,
0424   const Scalar &x0221, const Scalar &x1221, const Scalar &x2221, const Scalar &x3221,
0425   const Scalar &x0321, const Scalar &x1321, const Scalar &x2321, const Scalar &x3321,
0426   const Scalar &x0031, const Scalar &x1031, const Scalar &x2031, const Scalar &x3031,
0427   const Scalar &x0131, const Scalar &x1131, const Scalar &x2131, const Scalar &x3131,
0428   const Scalar &x0231, const Scalar &x1231, const Scalar &x2231, const Scalar &x3231,
0429   const Scalar &x0331, const Scalar &x1331, const Scalar &x2331, const Scalar &x3331,
0430   const Scalar &x0002, const Scalar &x1002, const Scalar &x2002, const Scalar &x3002,
0431   const Scalar &x0102, const Scalar &x1102, const Scalar &x2102, const Scalar &x3102,
0432   const Scalar &x0202, const Scalar &x1202, const Scalar &x2202, const Scalar &x3202,
0433   const Scalar &x0302, const Scalar &x1302, const Scalar &x2302, const Scalar &x3302,
0434   const Scalar &x0012, const Scalar &x1012, const Scalar &x2012, const Scalar &x3012,
0435   const Scalar &x0112, const Scalar &x1112, const Scalar &x2112, const Scalar &x3112,
0436   const Scalar &x0212, const Scalar &x1212, const Scalar &x2212, const Scalar &x3212,
0437   const Scalar &x0312, const Scalar &x1312, const Scalar &x2312, const Scalar &x3312,
0438   const Scalar &x0022, const Scalar &x1022, const Scalar &x2022, const Scalar &x3022,
0439   const Scalar &x0122, const Scalar &x1122, const Scalar &x2122, const Scalar &x3122,
0440   const Scalar &x0222, const Scalar &x1222, const Scalar &x2222, const Scalar &x3222,
0441   const Scalar &x0322, const Scalar &x1322, const Scalar &x2322, const Scalar &x3322,
0442   const Scalar &x0032, const Scalar &x1032, const Scalar &x2032, const Scalar &x3032,
0443   const Scalar &x0132, const Scalar &x1132, const Scalar &x2132, const Scalar &x3132,
0444   const Scalar &x0232, const Scalar &x1232, const Scalar &x2232, const Scalar &x3232,
0445   const Scalar &x0332, const Scalar &x1332, const Scalar &x2332, const Scalar &x3332,
0446   const Scalar &x0003, const Scalar &x1003, const Scalar &x2003, const Scalar &x3003,
0447   const Scalar &x0103, const Scalar &x1103, const Scalar &x2103, const Scalar &x3103,
0448   const Scalar &x0203, const Scalar &x1203, const Scalar &x2203, const Scalar &x3203,
0449   const Scalar &x0303, const Scalar &x1303, const Scalar &x2303, const Scalar &x3303,
0450   const Scalar &x0013, const Scalar &x1013, const Scalar &x2013, const Scalar &x3013,
0451   const Scalar &x0113, const Scalar &x1113, const Scalar &x2113, const Scalar &x3113,
0452   const Scalar &x0213, const Scalar &x1213, const Scalar &x2213, const Scalar &x3213,
0453   const Scalar &x0313, const Scalar &x1313, const Scalar &x2313, const Scalar &x3313,
0454   const Scalar &x0023, const Scalar &x1023, const Scalar &x2023, const Scalar &x3023,
0455   const Scalar &x0123, const Scalar &x1123, const Scalar &x2123, const Scalar &x3123,
0456   const Scalar &x0223, const Scalar &x1223, const Scalar &x2223, const Scalar &x3223,
0457   const Scalar &x0323, const Scalar &x1323, const Scalar &x2323, const Scalar &x3323,
0458   const Scalar &x0033, const Scalar &x1033, const Scalar &x2033, const Scalar &x3033,
0459   const Scalar &x0133, const Scalar &x1133, const Scalar &x2133, const Scalar &x3133,
0460   const Scalar &x0233, const Scalar &x1233, const Scalar &x2233, const Scalar &x3233,
0461   const Scalar &x0333, const Scalar &x1333, const Scalar &x2333, const Scalar &x3333
0462  ){
0463  \brief Special Constructor, templated in Scalar, taking 256 single components.
0464 */
0465
0466 #endif